diff --git a/src/library/definitional/equations.cpp b/src/library/definitional/equations.cpp
index ee35c93b7..ad91d9694 100644
--- a/src/library/definitional/equations.cpp
+++ b/src/library/definitional/equations.cpp
@@ -19,6 +19,7 @@ Author: Leonardo de Moura
 #include "library/io_state_stream.h"
 #include "library/annotation.h"
 #include "library/util.h"
+#include "library/locals.h"
 #include "library/tactic/inversion_tactic.h"
 
 namespace lean {
@@ -338,23 +339,16 @@ class equation_compiler_fn {
         }
     };
 
-    // For debugging purposes
-    template<typename T>
-    static bool contains_local(T const & locals, expr const & l) {
-        return std::any_of(locals.begin(), locals.end(),
-                           [&](expr const & l1) { return mlocal_name(l1) == mlocal_name(l); });
-    }
-
 #ifdef LEAN_DEBUG
     // For debugging purposes: checks whether all local constants occurring in \c e
     // are in local_ctx or m_global_context
     bool check_ctx(expr const & e, list<expr> const & context, list<expr> const & local_context) const {
         for_each(e, [&](expr const & e, unsigned) {
                 if (is_local(e) &&
-                    !(contains_local(local_context, e) ||
-                      contains_local(context, e) ||
-                      contains_local(m_global_context, e) ||
-                      contains_local(m_fns, e))) {
+                    !(contains_local(e, local_context) ||
+                      contains_local(e, context) ||
+                      contains_local(e, m_global_context) ||
+                      contains_local(e, m_fns))) {
                     lean_unreachable();
                     return false;
                 }
@@ -617,10 +611,6 @@ class equation_compiler_fn {
         return r;
     }
 
-    static bool contains(list<expr> const & local_ctx, expr const & p) {
-        return std::any_of(local_ctx.begin(), local_ctx.end(), [&](expr const & l) { return mlocal_name(l) == mlocal_name(p); });
-    }
-
     expr compile_skip(program const & prg) {
         lean_assert(!head(prg.m_var_stack));
         auto new_stack     = tail(prg.m_var_stack);
@@ -646,7 +636,7 @@ class equation_compiler_fn {
                 new_eqs.emplace_back(e.m_local_context, tail(e.m_patterns), e.m_rhs);
             } else {
                 lean_assert(is_local(p));
-                if (contains(e.m_local_context, p)) {
+                if (contains_local(p, e.m_local_context)) {
                     list<expr> new_local_ctx = e.m_local_context;
                     new_local_ctx      = remove(new_local_ctx, p);
                     new_local_ctx      = map(new_local_ctx, [&](expr const & l) { return replace(l, p, x); });
@@ -796,7 +786,7 @@ class equation_compiler_fn {
         }
     }
 
-    expr compile(program const & p) {
+    expr compile_pat_match(program const & p) {
         buffer<expr> vars;
         to_buffer(p.m_context, vars);
         if (!is_proof_irrelevant()) {
@@ -812,11 +802,7 @@ class equation_compiler_fn {
 
     /** \brief Return true iff \c e is one of the functions being defined */
     bool is_fn(expr const & e) const {
-        return
-            is_local(e) &&
-            std::any_of(m_fns.begin(), m_fns.end(), [&](expr const & fn) {
-                    return mlocal_name(fn) == mlocal_name(e);
-                });
+        return is_local(e) && contains_local(e, m_fns);
     }
 
     /** \brief Return true iff the equations are recursive. */
@@ -833,18 +819,39 @@ class equation_compiler_fn {
         return false;
     }
 
-    /** \brief Return true iff \c t is an inductive datatype (I A j) which constains an associated brec_on definition*/
-    bool is_inductive(expr const & t) const {
-        expr const & fn = get_app_fn(t);
-        return
-            is_constant(fn) &&
-            env().find(name{const_name(fn), "brec_on"});
+    /** \brief Return true if all locals are distinct local constants. */
+    static bool all_distinct_locals(unsigned num, expr const * locals) {
+        for (unsigned i = 0; i < num; i++) {
+            if (!is_local(locals[i]))
+                return false;
+            if (contains_local(locals[i], locals, locals + i))
+                return false;
+        }
+        return true;
+    }
+
+    /** \brief Return true iff \c t is an inductive datatype (I A j) which constains an associated brec_on definition,
+        and all indices of t are in ctx. */
+    bool is_rec_inductive(list<expr> const & ctx, expr const & t) const {
+        expr const & I = get_app_fn(t);
+        if (is_constant(I) && env().find(name{const_name(I), "brec_on"})) {
+            unsigned nindices = *inductive::get_num_indices(env(), const_name(I));
+            if (nindices > 0) {
+                buffer<expr> args;
+                get_app_args(I, args);
+                return
+                    all_distinct_locals(nindices, args.end() - nindices) &&
+                    std::all_of(args.end() - nindices, args.end(), [&](expr const & idx) { return contains_local(idx, ctx); });
+            } else {
+                return true;
+            }
+        } else {
+            return false;
+        }
     }
 
     /** \brief Return true iff t1 and t2 are inductive datatypes of the same mutually inductive declaration. */
     bool is_compatible_inductive(expr const & t1, expr const & t2) {
-        lean_assert(is_inductive(t1));
-        lean_assert(is_inductive(t2));
         buffer<expr> args1, args2;
         name const & I1 = const_name(get_app_args(t1, args1));
         name const & I2 = const_name(get_app_args(t2, args2));
@@ -986,7 +993,7 @@ class equation_compiler_fn {
                 expr const & v = p.get_var(*n);
                 expr const & t = mlocal_type(v);
                 if (// argument must be an inductive datatype
-                    is_inductive(t) &&
+                    is_rec_inductive(p.m_context, t) &&
                     // argument must be an inductive datatype different from the ones in arg_types
                     std::all_of(arg_types.begin(), arg_types.end(),
                                 [&](expr const & prev_type) { return !is_same_inductive(t, prev_type); }) &&
@@ -1011,23 +1018,149 @@ class equation_compiler_fn {
         return find_rec_args(prgs, 0, arg_pos, arg_types);
     }
 
-    void apply_brec_on(buffer<program> & prgs) {
+    expr compile_brec_on(buffer<program> & prgs) {
         lean_assert(!prgs.empty());
         buffer<unsigned> arg_pos;
         if (!find_rec_args(prgs, arg_pos)) {
             throw_error(sstream() << "invalid recursive equations, failed to find recursive arguments that are structurally smaller "
                         << "(possible solution: use well-founded recursion)");
         }
-        // out() << "Found recursive arguments: ";
-        // for (unsigned p : arg_pos) out() << " " << p; out() << "\n";
 
-        // TODO(Leo):
+        // Return the recursive argument of the i-th program
+        auto get_rec_arg = [&](unsigned i) -> expr {
+            program const & pi = prgs[i];
+            return get_ith(pi.m_context, arg_pos[i]);
+        };
+
+        // Return the type of the recursive argument of the i-th program
+        auto get_rec_type = [&](unsigned i) -> expr {
+            return mlocal_type(get_rec_arg(i));
+        };
+
+        // Return the program associated with the inductive datatype named I_name.
+        // Return none if there isn't one.
+        auto get_prg_for = [&](name const & I_name) -> optional<unsigned> {
+            for (unsigned i = 0; i < prgs.size(); i++) {
+                expr const & t = get_rec_type(i);
+                if (const_name(get_app_fn(t)) == I_name)
+                    return optional<unsigned>(i);
+            }
+            return optional<unsigned>();
+        };
+
+        expr const & a0_type = get_rec_type(0);
+        lean_assert(is_rec_inductive(prgs[0].m_context, a0_type));
+        buffer<expr> a0_type_args;
+        expr const & I0      = get_app_args(a0_type, a0_type_args);
+        inductive::inductive_decls t = *inductive::is_inductive_decl(env(), const_name(I0));
+        unsigned nparams                      = std::get<1>(t);
+        list<inductive::inductive_decl> decls = std::get<2>(t);
+
+        // Distribute parameters of the ith program intro three groups:
+        //    indices, major premise (arg), and remaining arguments (rest)
+        auto distribute_context = [&](unsigned i, buffer<expr> & indices, expr & arg, buffer<expr> & rest) {
+            program const & p      = prgs[i];
+            arg                    = get_rec_arg(i);
+            list<expr> const & ctx = p.m_context;
+            buffer<expr> arg_args;
+            get_app_args(mlocal_type(arg), arg_args);
+            lean_assert(nparams <= arg_args.size());
+            indices.append(arg_args.size() - nparams, arg_args.data() + nparams);
+            for (expr const & l : ctx) {
+                if (mlocal_name(l) != mlocal_name(arg) && !contains_local(l, indices))
+                    rest.push_back(l);
+            }
+        };
+
+        // Compute the resulting universe level for brec_on
+        auto get_brec_on_result_level = [&]() -> level {
+            buffer<expr> indices, rest;
+            expr arg;
+            distribute_context(0, indices, arg, rest);
+            expr r_type = Pi(indices, prgs[0].m_type);
+            return sort_level(m_tc.ensure_type(r_type).first);
+        };
+
+        level rlvl          = get_brec_on_result_level();
+        levels brec_on_lvls = cons(rlvl, const_levels(I0));
+        expr brec_on        = mk_constant(name{const_name(I0), "brec_on"}, brec_on_lvls);
+        buffer<expr> params;
+        // add parameters
+        for (unsigned i = 0; i < nparams; i++) {
+            params.push_back(a0_type_args[i]);
+            brec_on = mk_app(brec_on, a0_type_args[i]);
+        }
+
+        buffer<expr> Cs; // brec_on "motives"
+        buffer<buffer<expr>> C_args_buffer;
+        for (inductive::inductive_decl const & decl : decls) {
+            name const & I_name = inductive::inductive_decl_name(decl);
+            expr C;
+            C_args_buffer.push_back(buffer<expr>());
+            buffer<expr> & C_args = C_args_buffer.back();
+            if (optional<unsigned> p_idx = get_prg_for(I_name)) {
+                buffer<expr> indices, rest; expr arg;
+                distribute_context(*p_idx, indices, arg, rest);
+                expr type = Pi(rest, prgs[*p_idx].m_type);
+                C_args.append(indices);
+                C_args.push_back(arg);
+                C = Fun(C_args, type);
+            } else {
+                expr type = whnf(infer_type(brec_on));
+                expr d    = binding_domain(type);
+                expr unit = mk_constant("unit", rlvl);
+                to_telescope_ext(d, C_args);
+                C = Fun(C_args, unit);
+            }
+            brec_on = mk_app(brec_on, C);
+            Cs.push_back(C);
+        }
+
+        // add functionals
+        unsigned i = 0;
+        for (inductive::inductive_decl const & decl : decls) {
+            name const & I_name = inductive::inductive_decl_name(decl);
+            expr below = mk_constant(name{I_name, "below"}, brec_on_lvls);
+            below      = mk_app(mk_app(below, params), Cs);
+            expr F;
+            buffer<expr> & C_args = C_args_buffer[i];
+            if (optional<unsigned> p_idx = get_prg_for(I_name)) {
+                program & prg_i = prgs[*p_idx];
+                buffer<expr> indices, rest; expr arg;
+                distribute_context(*p_idx, indices, arg, rest);
+                below           = mk_app(mk_app(below, indices), arg);
+                expr b          = mk_local(mk_fresh_name(), "b", below, binder_info());
+                buffer<expr> new_ctx;
+                new_ctx.append(indices);
+                new_ctx.push_back(arg);
+                new_ctx.push_back(b);
+                new_ctx.append(rest);
+                prg_i.m_context = to_list(new_ctx);
+                // TODO(Leo): replace recursive calls with "b" applications
+                F               = compile_pat_match(prg_i);
+            } else {
+                expr star    = mk_constant(name{"unit", "star"}, rlvl);
+                buffer<expr> F_args;
+                F_args.append(C_args);
+                below        = mk_app(below, F_args);
+                F_args.push_back(mk_local(mk_fresh_name(), "b", below, binder_info()));
+                F = Fun(F_args, star);
+            }
+            brec_on = mk_app(brec_on, F);
+            i++;
+        }
+
+        // out() << "brec_on: " << brec_on << "\n";
+
+        return brec_on;
     }
 
-    void apply_wf(buffer<program> & /* prgs */) {
+    expr compile_wf(buffer<program> & /* prgs */) {
         // TODO(Leo)
+        return expr();
     }
 
+
 public:
     equation_compiler_fn(type_checker & tc, io_state const & ios, expr const & meta, expr const & meta_type, bool relax):
         m_tc(tc), m_ios(ios), m_meta(meta), m_meta_type(meta_type), m_relax(relax) {
@@ -1041,21 +1174,14 @@ public:
         initialize(eqns, prgs);
         if (is_recursive(prgs)) {
             if (is_wf_equations(eqns)) {
-                apply_wf(prgs);
+                return compile_wf(prgs);
             } else {
-                apply_brec_on(prgs);
+                return compile_brec_on(prgs);
             }
+        } else {
+            lean_assert(prgs.size() == 1);
+            return compile_pat_match(prgs[0]);
         }
-        buffer<expr> rs;
-        for (program const & p : prgs) {
-            expr r = compile(p);
-            // out() << r << "\nType: " << m_tc.infer(r).first << "\n";
-            rs.push_back(r);
-        }
-        if (closed(rs[0]))
-            return rs[0];
-        else
-            return m_meta;
     }
 };